The Leaning Tower of Pisa is 56.84 meters long. In the 1990’s, engineers restored the building so that angle y changed from 5.5° to 3.99°. To the nearest hundredth of a meter, how much did the restoration change the height of the Leaning Tower of Pisa?

**The height of the tower is adjacent to ∠ y.**

The length of the tower is the hypotenuse of the triangle created.

The length of the tower is the hypotenuse of the triangle created.

**adjacent**

——————— = cosine of ∠y

hypotenuse

——————— = cosine of ∠y

hypotenuse

**Let x be the height of the tower (the adjacent side to angle y).**

**If the angle was 5.5°,**

x

—————— = cos 5.5°

56.84

x

—————— ≈ 0.995396198367 {evaluated cosine of 5.5°}

56.84

x ≈ 56.58 {multiplied each side by 56.84}

**If the angle was 3.99°,**

x

—————— = cos 3.99°

56.84

x

—————— ≈ 0.997576209867 {evaluated cosine of 3.99°}

56.84

x ≈ 56.7 {multiplied each side by 56.84}

__Change in height__= 56.7 - 56.58

=

**0.12 m**

__Ask Algebra House__